Question

arătați ca numărul n=27^9×32^11:2-16^6×2×6^27 este pătrat perfect ​

Answer 1

n = 27^9 × 32^11 : 2 - 16^6 × 2 × 6^27 = (3^3)^9 × (2^5)^11 : 2 - (2^4)^6 × 2 × (2×3)^27 = 3^27 × 2^55 : 2 - 2^24 × 2 × 2^27 × 3^27 = 3^27 × 2^54 - 2^52 × 3^27 = 2^52 × 3^27 × (2^2 - 1) = 2^52 × 3^27 × 3 = 2^52 × 3^28 = (2^26 × 3^14)^2, deci este pătrat perfect